Today, a mathematician misses the point. The University
of Houston's College of Engineering presents this series
about the machines that make our civilization run, and
the people whose ingenuity created them.

A surprising number of otherwise
educated people have never studied calculus. They don't
know what it does or what it's for. Calculus is a form of
math that deals specifically with change.

For example, suppose you open a plug in the bottom of a
tank. You can use calculus to find out how long it'll
take to drain as the water level drops. If I floor the
accelerator, and I know my car's maximum acceleration at
any speed, then the calculus will tell me how fast I'll
be going after, say, eight seconds.

Now I've just found a disturbing old book from 1824,
entitled A Short View of the First Principles of the
Differential Calculus. It's by the Rev. Arthur Browne
at Cambridge University. Browne begins with a long
Preface, setting out his objectives. He's teaching
calculus to young men who'll go on to become clerics,
lawyers, and statesmen. That situation worries him.

He allows that it's important for students to develop a
sense of logic and order, but is calculus worth the
trouble? He concludes that it probably is not,
except as a brief exercise in logic, undistracted by any
problem-solving. So he gives us two hundred pages of
propositions and demonstrations. No hierarchy of ideas!
The last words on the last page are merely the end of a
dangling
calculation about the curvature of a parabola. He
says nothing whatsoever about the subject's utility.

In his Preface, Browne mentions that some people are
anxious to see Cambridge become "eminent in scientific pursuits."
That strikes him as nonsense. The only purpose
of universities, he says, is
"that they may continually yield a supply of men, well qualified to fill the various offices, both in Church and State."

What is so odd about Browne's cynicism is that Cambridge
was just becoming the focus of a mathematical revolution
in England. The great astronomer John Herschel had finished his studies
in mathematics in 1814. He'd stayed on to translate
French work in math. France was
then far ahead of England in mathematics, and Browne
took particular care to sneer at highfalutin French
mathemeticians.

Herschel's friend Charles
Babbage, inventor of the first programmable computer,
also finished math at Cambridge. Both were driving
England toward a deeper understanding of math and of its
use.

Browne shows us how we can miss the vitality around us by
trying to freeze the world in place. So much life swirled
about him in 1824. Cambridge, the calculus, learning
itself -- they were all energized by a world in motion, a
world changing. The new calculus had already become, for
Browne, a virtue that lay beyond either utility or
evolution. College was about serving a static nation with
the same students who had served that nation last year.

I went looking for Browne in biographical encyclopedias.
He was not to be found. The calculus is, as I said, about
change. And Browne was one of those who chose to be left
behind by change.

I'm John Lienhard, at the University of Houston, where
we're interested in the way inventive minds work.

(Theme music)

Browne, the Rev. A., A Short View of the First
Principles of the Differential Calculus. Cambridge: J.
Deighton & Sons, Cambridge, 1824